Question 546144
Square root of quantity {{{sqrt(3x+7)}}} = x - 1 
Square both sides
3x + 7 = (x-1)^2
FOIL the right side
3x + 7 = x^2 - 2x + 1
Combine like terms on the right
0 = x^2 - 2x - 3x + 1 - 7
A quadratic equation
x^2 - 5x - 6 = 0
Factors to
(x-6)(x+1) = 0
Two solutions
x = 6
x = -1
Check both solutions in the original equation
x=6
{{{sqrt(3(6)+7)}}} = 6 - 1 
{{{sqrt(25)}}} = 6 - 1 
5 = 5; x=6 is a good solution
x=-1
{{{sqrt(3(-1)+7)}}} = -1 - 1 
{{{sqrt(4)}}} = -2
2 = -2, an extraneous solution